Ergodic properties of generalized Lüroth series

Jose Barrionuevo; Robert M. Burton; Karma Dajani; Cor Kraaikamp

Acta Arithmetica (1996)

  • Volume: 74, Issue: 4, page 311-327
  • ISSN: 0065-1036

How to cite

top

Jose Barrionuevo, et al. "Ergodic properties of generalized Lüroth series." Acta Arithmetica 74.4 (1996): 311-327. <http://eudml.org/doc/206855>.

@article{JoseBarrionuevo1996,
author = {Jose Barrionuevo, Robert M. Burton, Karma Dajani, Cor Kraaikamp},
journal = {Acta Arithmetica},
keywords = {ergodic properties; construction of generalized Lüroth series; transformations},
language = {eng},
number = {4},
pages = {311-327},
title = {Ergodic properties of generalized Lüroth series},
url = {http://eudml.org/doc/206855},
volume = {74},
year = {1996},
}

TY - JOUR
AU - Jose Barrionuevo
AU - Robert M. Burton
AU - Karma Dajani
AU - Cor Kraaikamp
TI - Ergodic properties of generalized Lüroth series
JO - Acta Arithmetica
PY - 1996
VL - 74
IS - 4
SP - 311
EP - 327
LA - eng
KW - ergodic properties; construction of generalized Lüroth series; transformations
UR - http://eudml.org/doc/206855
ER -

References

top
  1. [B] J. R. Brown, Ergodic Theory and Topological Dynamics, Academic Press, New York, 1976. Zbl0334.28011
  2. [BJW] W. Bosma, H. Jager and F. Wiedijk, Some metrical observations on the approximation by continued fractions, Indag. Math. 45 (1983), 281-299. Zbl0519.10043
  3. [CFS] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Grundlehren Math. Wiss. 245, Springer, New York, 1982. 
  4. [FS] C. Frougny and B. Solomyak, Finite beta-expansions, Ergodic Theory Dynamical Systems 12 (1992), 713-723. Zbl0814.68065
  5. [G] J. Galambos, Representations of Real Numbers by Infinite Series, Lecture Notes in Math. 502, Springer, Berlin, 1982. Zbl0322.10002
  6. [J] H. Jager, On decimal expansions, Zahlentheorie, Berichte aus dem Mathematische Forschungsinstitut Oberwolfach 5 (1971), 67-75. 
  7. [JdV] H. Jager and C. de Vroedt, Lüroth series and their ergodic properties, Indag. Math. 31 (1968), 31-42. Zbl0167.32201
  8. S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, Lüroth-type alternating series representations for real numbers, Acta Arith. 55 (1990), 311-322. Zbl0702.11048
  9. S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, Metric properties of alternating Lüroth series, Portugal. Math. 48 (1991), 319-325. Zbl0735.11035
  10. [K] C. Kraaikamp, A new class of continued fraction expansions, Acta Arith. 57 (1991), 1-39. Zbl0721.11029
  11. [Li] P. Liardet, MR: 93m:11077. 
  12. [Lu] J. Lüroth, Ueber eine eindeutige Entwickelung von Zahlen in eine unendliche Reihe, Math. Ann. 21 (1883), 411-423. 
  13. [Pa] W. Parry, On the β-expansions of real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960), 401-416. Zbl0099.28103
  14. [Pe] O. Perron, Irrationalzahlen, de Gruyter, Berlin, 1960. 
  15. [R] V. A. Rohlin, Exact endomorphisms of a Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 24 (1960) (in Russian); English translation: Amer. Math. Soc. Transl. Ser. 2, 39 (1969), 1-36. 
  16. [Sa] T. Šalát, Zur metrischen Theorie der Lürothschen Entwicklungen der reellen Zahlen, Czech. Math. J. 18 (1968), 489-522. Zbl0162.34703
  17. [So] B. Solomyak, Personal communication with C. Kraaikamp, Seattle, July 9, 1991. 
  18. [V] W. Vervaat, Success Epochs in Bernoulli Trails with Applications in Number Theory, Math. Centre Tracts 42, Amsterdam, 1972. Zbl0267.60003
  19. [W] P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, New York, 1982. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.